THE PROBABILISTIC STUDY OF VOLTAGE PROBLEMS IN LIGHTLY LOADED MEDIUM VOLTAGE POWER SYSTEM CONNECTED WITH SMALL CHP GENERATORS

Transcription

1 C I R E D 17 th International Conference on Electricity Distribution Barcelona, 1-15 May 3 THE PROBABILISTIC STUDY OF VOLTAGE PROBLEMS IN LIGHTLY LOADED MEDIUM VOLTAGE POWER SYSTEM CONNECTED WITH SMALL CHP GENERATORS Marian SOBIERAJSKI Wroclaw University of Technology - Poland marsobwp@wp.pl Wilhelm ROJEWSKI Wroclaw University of Technology - Poland rojewski@elektryk.ie.pwr.wroc.pl INTRODUCTION New requirements and constraints in voltage regulation in the vicinity of dispersed generation imply using new methods of power network analysis. Especially, the uncertainty of load demand should be taken into consideration. In this paper, the probabilistic method of load flow is proposed to be used for steady state analysis of local generation connected to the MV network. The probabilistic load flow results were taken as the basis for the experiment to increase the active power of CHP generators from.7 to 5.. Bus Bus voltage Un Gen. P Gen. Q Load P Load Q HV 11 kv slack slack - - MV kv SL kv CHP kv Abbreviations used in Tab. 1 have the following meaning: HV- High Voltage Source, MV - Middle Voltage Source, SL - Small Load, U n -the nominal voltage. CHP SL MV THE STUDIED MV POWER SYSTEM G1 G HV It is well known that the middle voltage distribution networks were designed to feed customers only from a high voltage power system. Local generation connected to the MV network is a new challenge for power planners and operators. The correct strategy for managing voltage regulation in the presence of local generation depends on the operation mode of the local generator (power factor or voltage control) and the on-load tap-changers control [-6]. Dispersed local generation can lead even to reverse active and reactive flows. According to planning and operation rules in Poland the customer bus voltage must not violate +5%, -1% of the nominal voltage U n for the MV network. Fulfilling these voltage limits produces the bottle neck in sending the whole CHP generation to the MV network, Fig. 1. The CHP generators work with the constant power factor equal 1. Only.7 (i.e. 5 %) of this generation can be sent to MV network without voltage limits violation. To achieve sending the whole CHP generation of 5.4 the study of probabilistic load flow were made and then the experiment of sending 5. was done. The relevant load and generation of the analysed MV power system are given in Tab. 1 and the scheme is presented in Fig. 1. Branch data are given in Tab.. Per unit (p.u.) values are related to the base power of 1 MVA and the nominal voltage U n at the To bus. TABLE 1 - Load and generation in the analysed MV power system FIGURE 1 - The studied MV power system TABLE - Branch data of the analysed power system From To R, p.u. X, p.u. B, p.u. HV MV MV SL CHP SL Voltage regulation at MV bus is achieved using on-load tapchangers having 19x1.5% taps giving a range of +/- 1% with tap 1 corresponding to the nominal ratio of 115/ kv. The maximal, minimal and step tap ratio are given in Tab. 3. TABLE 3 - Tap-changer data Min. tap ratio Max. tap ratio Step tap ratio CHP generators work with the constant power factor equal 1, which means that the unit transformers consume reactive power from the power system. From the point of view of the load flow analysis the active generation of CHP can be considered as negative load. A dilemma can arise between the required active power output of the CHP generation, the need to maintain system voltage within 1%/+5% limits and the 1 power factor of the WUT_Sobierajski_A1 Session 4 Paper No

2 C I R E D 17 th International Conference on Electricity Distribution Barcelona, 1-15 May 3 CHP generators. In order to compensate for the voltage drop in the distribution system between the MV bus and the consumers due to load currents, the voltage at the MV bus is proposed to be boosted as the load current increases, according to the following formula U = U preset kr c P/U + kx c P (1) U the voltage magnitude at MV bus, U the preset voltage magnitude at MV bus, R c the compensation circuit resistance, X c the compensation circuit reactance, k the modelling coefficient, P the active transformer flow, Q the reactive transformer flow. This compensation is accomplished using Automatic Voltage Control of tap changer, which increases the output voltage target in proportion to the load current. The resistance of AVC was set to zero R c = Ω and reactance X c = 1 Ω. The zero resistance was chosen to avoid the voltage change due to increase of reactive power flow in the transformer. To control the MV bus, the reference voltage was preset to be U preset = 1 while the bandwith is +/- %. The time delay was set to T delay = 18s to avoid hunting and to minimize excessive tap-changer operations and consequent wear and tear. Before the experiment, the probabilistic study of load flows in the power system was done to find the probability of the violation of voltage constraints. From the observations it was noticed that the active CHP generation can change +/-.1% and the reactive CHP generation can change much more to +/-5% because of forcing the power factor to 1. The complex load at SL bus and load at MV bus can change +/-5% due to random demand. Generally, the generation and loads are treated as the random vector distributed in given ranges y min < y < y max () The rectangular probability distribution of bus loads is assumed as a pessimistic one. So the bus loads are described by Ey - the vector of expected value and My - the covariance matrix. PROBABILISTIC LOAD FLOW BACKGROUND It is well known that the deterministic load flow can be calculated by solving the set of nonlinear algebraic equations. P i = U i G ii +Σ[ G ij cos(δ i -δ j ) + B ij sin(δ i -δ j ) ] (3) Q i = -U i B ii +Σ[-B ij cos(δ i -δ j ) + G ij sin(δ i -δ j ) ] (4) P i the given active power at bus i, Q i the given reactive power at bus i, U i the unknown voltage magnitude at bus i, δ i the unknown voltage angle at bus i, G ij the mutual bus conductance, B ij the mutual bus susceptance, G ii the self bus conductance, B ii the self bus susceptance, As it was previously mentioned, the active and reactive power at all buses may be treated as random variables. In the most pessimistic case the random values of powers may be treated as rectangularly distributed in the range Then we have - expected value of active power P min P P max (5) Q min Q Q max (6) E(P) = (P max - P min )/ (7) - expected value of reactive power - variance of active power - variance of reactive power E(Q) =(Q max - Q min )/ (8) m PP = σ P = (P max - P min ) /1 (9) m QQ = σ Q = (Q max - Q min ) /1 (1) The bus power are treated as the independent random variables what means that their covariance is equal to zero m PQ = (11) The variances and covariances create the covariance matrix m PP m PQ M y = (1) m PQ m QQ The covariance matrix in this case is the diagonal matrix WUT_Sobierajski_A1 Session 4 Paper No

3 C I R E D 17 th International Conference on Electricity Distribution Barcelona, 1-15 May 3 M y m = PP m QQ (13) The randomness of load powers involves the randomness of the bus voltage magnitudes and angles. The easiest way to calculate the expected values, variances and covariances of bus voltages is a linearization of load flow equations [1]. The bus powers are treated as the random variables, so generally we have x = A -1 y () Then the covariance matrix of the bus voltage is equal M x = A -1 M y A -1 T (3) So, the bus voltages are treated as the linear transformation of uniformly distributed bus powers. It means that the bus voltages are the random variables, which are subjected to the normal probability distribution y = f(x) (14) y the vector of random bus powers, x the vector of unknown random bus voltages, f the nonlinear function. 1 (x Ex) N (Ex, σ) = exp (4) σ π σ σ - the standard deviation of the voltage magnitude. Using Taylor series around the unknown expected values of bus voltages Ex we have y f(ex) + A(x-Ex) (15) The probability of the violation of voltage constraint x min x x max (5) Ex - the vector of the expected value of unknown bus voltages, A - the Jacobian calculated at the point of Ex. The formula (15) may be rewritten as y - f(ex) = A(x-Ex) (16) is equal p{x min x x max } =.5F(t b )-.5F(t a ) (6) t = (x - Ex)/σ (7) or y = A x (17) y = y Ey the vector of bus load deviations, x = x Ex the vector of bus voltage deviations. The expected value of deviation is equal zero E y = E(y-Ey) = Ey - Ey = (18) E x = E(x-Ex) = Ex - Ex = (19) t F (t) = exp( z / )dz (8) π According to the 3-sigma rule we can estimate the minimal and maximal value of the bus voltages with the probability of.9973 as x min = Ex - 3σ (9) x max = Ex + 3σ (3) so, it means that we have for the expected values Ey = f(ex) () The unknown expected value of bus voltages can be calculated iteratically using the Newton method Ex new = Ex old + A old -1 -[Ey - f(ex ld )] (1) The deviations of bus voltages can be calculated using the inverse of the Jacobian at the point of Ex WUT_Sobierajski_A1 Session 4 Paper No

4 C I R E D 17 th International Conference on Electricity Distribution Barcelona, 1-15 May 3 PROBABILISTIC LOAD FLOW CALCULATIONS Before the experiment of sending 5. into the MV network the probabilistic load flow study was done to find the probability of the violation of the bus voltage constraints. In Tab. 4 the random ranges of bus powers, which were taken into account, are given. The CHP generation was considered as the negative loads. TABLE 4 - Random bus powers Bus Pmax Pmin EP Qmax Qmin EQ MV SL CHP The symbols EP mean the expected value of the active bus power and EQ - the expected value of the reactive bus power. First of all the covariance matrix of the bus power M y and then the covariance matrix of the bus voltages M x were computed. The results of the probabilistic load flow are given in Tab. 5 and in Fig.. TABLE 5 - Random bus voltages from probabilistic load flow Bus Umax Umin EU p(u>1.5un) p.u. p.u. p.u. MV SL CHP The symbol EU means the expected value of the bus voltage magnitude and p - the probability. of the violation of the 1.5U n voltage magnitude at the CHP bus is about.43. RESULTS OF EXPERIMENT On 6th September, from 11.3 till 1., CHP generators were forced to send the active power of 5. into the MV network with power factor equal 1. The active and reactive generation and the bus voltage magnitude at CHP bus were measured every 1 minute. The results are given in Tab. 6 and 7 and in Fig. 3 and 4. It is seen that the results obtained from the probabilistic load flow study are much more pessimistic than the similar results obtained from the experiment. It concerns the maximal and minimal value of bus voltage magnitude and the probability of the violation of the bus voltage magnitude constraints. The reason for these differences comes mainly from the assumption of the rectangular distribution of bus power and the error of the linearization of load flow equations. TABLE 6 - Random bus powers obtained from the experiment and the probabilistic voltage study Bus case EP σ P EQ σ Q CHP Experiment CHP Probabilistic load flow Q,Mvar Reactive generation of CHP Station U,p.u. Random voltage magnitude time, min.9 CHP SL MV 1 Number of elements Histogram of reactive generation.5 Probability Probability of U > 1.5Un Q,Mvar.1 MV SL MV FIGURE - Random voltage magnitude from the probabilistic load flow From Tab. 5 and Fig. it is clearly seen that during the experiment one should take into account that the probability FIGURE 3 - Reactive generation during the experiment From Fig. 3 it is seen that the probability distribution of the reactive generation may be roughly treated as a rectangular distribution. WUT_Sobierajski_A1 Session 4 Paper No

5 C I R E D 17 th International Conference on Electricity Distribution Barcelona, 1-15 May 3 TABLE 7 - Random bus voltages from probabilistic load flow study Bus case Umax Umin EU p(u>1.5un) pu pu pu CHP Experiment CHP Probabilistic load flow From the histogram of the voltage magnitude (Fig. 4) one can suppose that the assumption of the normal probability distribution of the voltage magnitude is a rather rough approximation. It may produce differences between empirical results and analytical results. The analytical results are based on the linearization of load flow equations and on the linear transformation of random variables. From the property of the linear transformation of rectangular distributed random bus powers it was concluded that the probability distribution of the voltage magnitude is a normal one. 1.6 pu Voltage magnitude at CHP Station 4. The results obtained from the probabilistic load flow study are much more pessimistic than obtained from the experiment. However they were a good basis for decisions during increasing the CHP generation from.7 to The probabilistic study of load flow is quick and it gives practical and concise results. REFERENCES [1] M. Sobierajski, 1978, A method of stochastic load flow calculations, Arch. f. Elektr., No. 1, [] H. Kirkham, R. Das, 1984, Effects of voltage control in utility interactive dispersed storage and generation systems, IEEE Trans. on PAS, Vol. PAS-13, No.8, time, min Histogram of voltage magnitude Number of elements [3] M.S. Calovic,1984, Modeling and analysis of underload tap-changing transformer control systems, IEEE Trans. on PAS, Vol. PAS-13, No.7, [4] J.H. Choi, J.C. Kim,, Advanced voltage regulation method at the power distribution systems interconnected with dispersed storage and generation systems, IEEE Trans. on Power Delivery, Vol. 15, No., [5] A. Bonhomme, D. Cortinas, F. Boulanger, J.L. Fraisse, 1, A new voltage control system to facilitate the connection of dispersed generation to distribution networks, Proceedings CIRED 1, Amsterdam, 18-1 June 1, paper Voltage U,pu FIGURE 4 - The bus voltage magnitude during experiment [6] G. Glendinning, 1, Potential solutions to voltage control issues for distribution networks connecting independent generators, Proceedings CIRED 1, Amsterdam, 18-1 June 1, paper 4.3. CONCLUSIONS 1. Local generation connected to the MV network is a new challenge for power planners and operators. The correct strategy for managing voltage regulation in the presence of local generation depends on the operation mode of the local generator (power factor or voltage control) and the on-load tap-changers control.. New requirements and constraints in voltage regulation in the vicinity of dispersed generation imply using new methods of power network analysis. Especially, the uncertainty of load demand should be taken into consideration. 3. In this paper, the probabilistic method of load flow is proposed to be used for steady state analysis of local generation connected to the MV network. The probabilistic load flow results were taken as the basis for the experiment to increase the active generation of CHP generators from.7 to 5.. WUT_Sobierajski_A1 Session 4 Paper No